You posted your question here in the Pediatrics sections but if you don't mind a pediatrician with 33 years experience treating kids through young adults giving you advice, here is my opinion:
Allergies do NOT cause a cough! Allergy symptoms range from runny and itchy nose and eyes to post-nasal drip that can make you hoarse and clear your throat a lot but cough is from the lungs, not the throat, nose or sinuses unless you either have an infection in your sinuses OR have asthma.
I suspect you have undiagnosed asthma.
The reason I say that is that, as with kids, chronic cough, even without wheezing and shortness of breath, often indicate bronchospasm and asthma consists of two components: bronchospasm that causes cough with or without wheezing AND inflammation in the small airways leading to mucous production.
I would ask your doctor to consider asthma and give you a trial of an inhaler with albuterol to see if that helps your cough.
I see you are still offline so I'll exit chat and move our discussion over to the normal Q&A mode to allow you time to return to the session. Otherwise, chat will time us out and kick us off if we are not both actively involved in the session.
I also forgot to add that 2 weeks into the cough i had what appeared to be an allergy related rash on upper arm that cleared in two days. The reason i say the rash could be allergy related is that it looked like a very bumpy bumpy goose bumps and was white. Im light skin and most rashes i have seen are red but the head of this one was white (hope you understood what im trying to say)
Hi Dr. Clark,
I got a chest X-Ray done last Friday and the results came back normal. What else could be the problem.